Estimating the density of a conditional expectation

In this paper, we analyze methods for estimating the density of a conditional expectation. We compare an estimator based on a straightforward application of kernel density estimation to a bias-corrected estimator that we propose. We prove convergence results for these estimators and show that the bias-corrected estimator has a superior rate of convergence. In a simulated test case, we show that the bias-corrected estimator performs better in a practical example with a realistic sample size.